Solving an equation of sums

I want to find y in an equation which has the following form:

1/(1+y)^1 + 1/(1+y)^2 + 1/(1+y)^3 + 1/(1+y)^4 + 1/(1+y)^5 + 1/(1+y)^6 + 1/(1+y)^7 = c

where c is a known constant real value.

Any help could be useful. thanks in advance!

Answer 1

[Torsten]

Use "roots" to calculate the real zero x0 of the polynomial

p(x)=x^8-(1+c)*x+c.

Then y0=1/x0-1 will solve your above equation.

Best wishes

Torsten.

[Konstantinos]

Thanks for the help!..but where did you find p(x) ?

[Torsten]

Geometric series:

x+x^2+x^3+x^4+x^5+x^6+x^7=(x^8-1)/(x-1) - 1 = (x^8-x)/(x-1)

with x=1/(1+y)

Best wishes

Torsten.

[Konstantinos]

Thanks a lot!!